Simplify the following expression: $ q = \dfrac{-t}{t + 10} - \dfrac{-9}{4} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-t}{t + 10} \times \dfrac{4}{4} = \dfrac{-4t}{4t + 40} $ Multiply the second expression by $\dfrac{t + 10}{t + 10}$ $ \dfrac{-9}{4} \times \dfrac{t + 10}{t + 10} = \dfrac{-9t - 90}{4t + 40} $ Therefore $ q = \dfrac{-4t}{4t + 40} - \dfrac{-9t - 90}{4t + 40} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-4t - (-9t - 90) }{4t + 40} $ Distribute the negative sign: $q = \dfrac{-4t + 9t + 90}{4t + 40}$ $q = \dfrac{5t + 90}{4t + 40}$